research-article

Skeletonization of Three-Dimensional Object Using Generalized Potential Field

Authors:

Min-Chi KoAuthors Info & Claims

IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 22, Issue 11

Pages 1241 - 1251

https://doi.org/10.1109/34.888709

Published: 01 November 2000 Publication History

Abstract

The medial axis transform (MAT) is a skeletal representation of an object which has been shown to be useful in interrogation, animation, finite element mesh generation, path planning, and feature recognition. In this paper, the potential-based skeletonization approach for 2D MAT [1], which identifies object skeleton as potential valleys using a Newtonian potential model in place of the distance function, is generalized to three dimensions. The generalized potential functions given in [2], which decay faster with distance than the Newtonian potential, is used for the 3D case. The efficiency of the proposed approach results from the fact that these functions and their gradients can be obtained in closed forms for polyhedral surfaces. According to the simulation results, the skeletons obtained with the proposed approach are closely related to the corresponding MAT skeletons. While the medial axis (surface) is 2D in general for a 3D object, the potential valleys, being one-dimensional, form a more realistic skeleton. Other desirable attributes of the algorithm include stability against perturbations of the object boundary, the flexibility to obtain partial skeleton directly, and low time complexity.

References

[1]

N. Ahuja and J.-H. Chuang, “Shape Representation Using a Generalized Potential Field Model,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 2, pp. 169-176, Feb. 1997.

Digital Library

[2]

J.-H. Chuang, “Potential-Based Modeling of Three Dimensional Workspace for Obstacle Avoidance,” IEEE Trans. Robotics and Automation, vol. 14, no. 5, pp. 778-785, 1998.

[3]

H. Blum, “A Transformation for Extracting New Descriptors of Shape,” Models for the Perception of Speech and Visual Form, W. Wathen-Dunn, ed., Cambridge, Mass.: MIT Press, 1967.

[4]

J.W. Brandt A.K. Jain and V.R. Algazi, “Medial Axis Representation and Encoding of Scanned Documents,” J. Visual Comm. and Image Representation, vol. 2, no. 2, pp. 151-165, June 1991.

[5]

H. Blum and R.N. Nagel, “Shape Description Using Weighted Symmetric Axis Features,” Pattern Recognition, vol. 10, no. 3, pp. 167-180, 1978.

[6]

A. Rosenfeld, “Axial Representations of Shape,” Computer Vision, Graphics, and Image Processing, vol. 33, pp. 156-173, 1986.

Digital Library

[7]

O. Takahashi and R.J. Schilling, “Motion Planning in a Plane Using Generalized Voronoi Diagrams,” IEEE Trans. Robotics and Automation, vol. 5, no. 2, pp. 143-150, 1989.

[8]

F.B. Prinz and J.-H. Chern, “Geometric Abstractions Using Medial Axis Transformation,” Technical Report EDRC-24-24-89 Eng. Design Research Center, Carnegie Mellon Univ., 1989.

[9]

H.N. Gursoy and N.M. Patrikalakkis, “An Automated Coarse and Fine Surface Mesh Generation Scheme Based on Medial Axis Transform, Part I: Algorithms,” Eng. with Computers, vol. 8, no. 3, pp. 121-137, 1992.

Digital Library

[10]

H.N. Gursoy and N.M. Patrikalakkis, “An Automated Coarse and Fine Surface Mesh Generation Scheme Based on Medial Axis Transform, Part II: Implementation,” Eng. with Computers, vol. 8, no. 4, pp. 179-196, 1992.

Digital Library

[11]

G. Turkiyyah and J. Fenves, “Generation and Interpretation of Finite Element Models in a Knowledge Based Environment,” Technical Report R-90-188 Dept. of Civil Eng., Carnegie Mellon Univ., 1990.

[12]

N. Ahuja L.S. Davis D.L. Milgram and A. Rosenfeld, “Piecewise Approximation of Pictures Using Maximal Neighborhoods,” IEEE Trans. Computers, vol. 27, pp. 375-379, 1978.

[13]

F. Meyer, “The Binary Skeleton in Three Steps,” Computer Architecture for Pattern Analysis and Image Database Management, New York: IEEE CS Press, 1985.

[14]

F. Meyer, “Skeletons and Perceptual Graphics,” Signal Processing, pp. 335-363, 1989.

[15]

A. Montanvert, “Medial Line, Graph Representation and Shape Description,” Proc. Eighth Int'l Conf. Pattern Recognition, pp. 430-432, 1986.

[16]

G. Borgefors, “Distances Transformations in Digital Images,” Computer Vision, Graphics, and Image Processing, vol. 34, pp. 344-371, 1986.

Digital Library

[17]

L. Dorst, “Pseudo-Euclidean Skeleton,” Proc. Eighth Int'l Conf. Pattern Recognition, pp. 286-288, 1986.

[18]

Y. Xia, “Skeletonization via the Realization of the Fire Front's Propagation and Extinction in Digital Binary Shapes,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, pp. 1,076-1,086, Nov. 1989.

Digital Library

[19]

U. Montanari, “Continuous Skeletons from Digitized Image,” J. ACM, vol. 14, pp. 534-549, 1969.

Digital Library

[20]

D.G. Kirkpatrick, “Efficient Computation of Continuous Skeletons,” Proc. 20th Ann. IEEE Symp. Foundations of Computer Science, pp. 18-27, Oct. 1979.

Digital Library

[21]

D.T. Lee, “Medial Axis Transformation of a Planar Shape,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 4, pp. 363-369, Apr. 1982.

Digital Library

[22]

L. Vincent, “Efficient Computation of Various Types of Skeletons,” SPIE Image Processing, vol. 1, 445, pp. 297-311, 1991.

[23]

D. Dutta and C.M. Hoffmann, “On the Skeleton of Simple CSG Objects,” ASME Trans. J. Mechanical Design, vol. 115, no. 1, pp. 87-94, Mar. 1993.

[24]

L.R. Nackman, “Curvature Relations in Three-Dimensional Symmetric Axes,” Computer Graphics and Image Processing, vol. 20, pp. 43-57, 1982.

[25]

J.W. Brandt and V.R. Algazi, “Continuous Skeleton Computation by Voronoi Diagram,” CVGIP: Image Understanding, vol. 55, no. 3, pp. 329-338, 1992.

Digital Library

[26]

D. Levender A. Bowyer J. Davenport A. Wallis and J. Woodwark, “Voronoi Diagrams of Set-Theoretic Solid Models,” IEEE Computer Graphics and Applications, vol. 12, no. 5, pp. 69-77, 1992.

Digital Library

[27]

J.M. Reddy and G.M. Turkiyyah, “Computation of 3D Skeletons Using a Generalized Delaunay Triangulation Technique,” Computer-Aided Design, vol. 27, no. 9, pp. 677-694, Sept. 1995.

[28]

D.J. Sheehy C.G. Armstrong and D.J. Robinson, “Shape Description by Medial Surface Construction,” IEEE Trans. Visualization and Computer Graphics, vol. 2, no. 1, pp. 62-73, Mar. 1996.

Digital Library

[29]

D. Attali P. Bertolino and A. Montanvert, “Using Polyballs to Approximate Shapes and Skeletons,” Proc. Int'l Conf. Pattern Recognition, Oct. 1994.

[30]

Y.F. Tsao and K.S. Fu, “A Parallel Thinning Algorithm for 3D Pictures,” Computer Graphics and Image Processing, vol. 17, pp. 315-331, 1981.

[31]

C.M. Ma, “A Fully Parallel Thinning Algorithm for Generating Medial Faces,” Pattern Recognition Letters, vol. 16, pp. 83-87, Jan. 1995.

Digital Library

[32]

C.M. Ma and M. Sonaka, “A Fully Parallel 3D Thinning Algorithm and Its Applications,” Computer Vision and Image Understanding, vol. 64, no. 3, pp. 420-433, Nov. 1996.

Digital Library

[33]

E.C. Sherbrooke N.M. Patrikalakis and E. Brisson, “An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids,” IEEE Trans. Visualization and Computer Graphics, vol. 2, no. 1, pp. 44-61, Mar. 1996.

Digital Library

[34]

J.-H. Chuang, “Skeletonization of Three-Dimensional Regions Using Generalized Potential Field,” Proc. Int'l Conf. Control and Robotics, Aug. 1992.

[35]

D.R. Wilton S.M. Rao A.W. Glisson D.H. Schaubert O.M. Al-Bundak and C.M. Butler, “Potential Integrals for Uniform and Linear Source Distributions on Polygonal and Polyhedral Domains,” IEEE Trans. Antennas and Propagation, vol. 32, no. 3, pp. 276-281, Mar. 1984.

[36]

G. Turk, “Re-Tiling Polygonal Surfaces,” Computer Graphics, vol. 26, no. 2, pp. 55-64, July 1992.

Digital Library

[37]

J.-C. Latombe, Robot Motion Planning. Kluwer Academic Publishers, 1991.

Digital Library

[38]

P.J. Vermeer, “Medial Axis Transform to Boundary Representation Conversion,” PhD Thesis, Purdue Univ., 1994.

Digital Library

[39]

T.O. Binford, “Visual Perception by Computer,” Proc. IEEE Systems Science and Cybernetics Conf., 1971.

Cited By

Chu YWang WLi L(2023)Robustly Extracting Concise 3D Curve Skeletons by Enhancing the Capture of Prominent FeaturesIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2022.316196229:8(3472-3488)Online publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1109/TVCG.2022.3161962
Liu MZhang YBai JCao YAlperovich JRamani KMark GFussell SLampe Cschraefel mHourcade JAppert CWigdor D(2017)WireFabProceedings of the 2017 CHI Conference on Human Factors in Computing Systems10.1145/3025453.3025619(965-976)Online publication date: 2-May-2017
https://dl.acm.org/doi/10.1145/3025453.3025619
Packer JHasan MSamavati F(2017)Illustrative multilevel focus+context visualization along snaking pathsThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-016-1217-033:10(1291-1306)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1007/s00371-016-1217-0
Show More Cited By

Index Terms

Skeletonization of Three-Dimensional Object Using Generalized Potential Field
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Computer vision representations
        Image representations
  2. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

Recommendations

The Groupwise Medial Axis Transform for Fuzzy Skeletonization and Pruning

Medial representations of shapes are useful due to their use of an object-centered coordinate system that directly captures intuitive notions of shape such as thickness, bending, and elongation. However, it is well known that an object's medial axis ...
Recognizing implicitly given rational canal surfaces

It is still a challenging task of today to recognize the type of a given algebraic surface which is described only by its implicit representation. In this paper we will investigate in more detail the case of canal surfaces that are often used in ...
IMMAT: Mesh Reconstruction from Single View Images by Medial Axis Transform Prediction
Abstract
The representation of a 3D shape is a key element for capturing the overall structure as well as the local details. In this paper, we propose to predict a mesh representation of the Medial Axis Transform (called medial mesh) as an ...
Graphical abstract

Display Omitted
Highlights
- We utilize medial axis transform for 3D reconstruction from single view images.

Comments

Information & Contributors

Information

Published In

cover image IEEE Transactions on Pattern Analysis and Machine Intelligence

IEEE Transactions on Pattern Analysis and Machine Intelligence Volume 22, Issue 11

November 2000

143 pages

ISSN:0162-8828

Editors:
Kevin Bowyer
Univ. of South Florida, Tampa
,
Patrick Flynn
Ohio State Univ., Columbus

Issue’s Table of Contents

Copyright © Copyright © 2000 IEEE. All Rights Reserved.

Publisher

IEEE Computer Society

United States

Publication History

Published: 01 November 2000

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

23
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 09 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Chu YWang WLi L(2023)Robustly Extracting Concise 3D Curve Skeletons by Enhancing the Capture of Prominent FeaturesIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2022.316196229:8(3472-3488)Online publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1109/TVCG.2022.3161962
Liu MZhang YBai JCao YAlperovich JRamani KMark GFussell SLampe Cschraefel mHourcade JAppert CWigdor D(2017)WireFabProceedings of the 2017 CHI Conference on Human Factors in Computing Systems10.1145/3025453.3025619(965-976)Online publication date: 2-May-2017
https://dl.acm.org/doi/10.1145/3025453.3025619
Packer JHasan MSamavati F(2017)Illustrative multilevel focus+context visualization along snaking pathsThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-016-1217-033:10(1291-1306)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1007/s00371-016-1217-0
Ismail MElshzaly SFarag ASites CCurtin RFalk RSeow ADryden G(2015)Revamped fly‐over for accurate colon visualisation in virtual colonoscopyIET Computer Vision10.1049/iet-cvi.2014.01779:4(511-521)Online publication date: 1-Aug-2015
https://dl.acm.org/doi/10.1049/iet-cvi.2014.0177
Walczak MBinkowski MSulikowska-Drozd AWróbel Z(2015)Maximum sphere method for shell patency measurements in viviparous land snails based on X-ray microcomputed tomography imagingComputers in Biology and Medicine10.1016/j.compbiomed.2015.06.00464:C(187-196)Online publication date: 1-Sep-2015
https://dl.acm.org/doi/10.1016/j.compbiomed.2015.06.004
Mehrdad VEbrahimnezhad H(2015)3D object retrieval based on histogram of local orientation using one-shot score support vector machineFrontiers of Computer Science: Selected Publications from Chinese Universities10.1007/s11704-015-4291-y9:6(990-1005)Online publication date: 1-Dec-2015
https://dl.acm.org/doi/10.1007/s11704-015-4291-y
Mehrdad VEbrahimnezhad H(2015)3D model retrieval based on linear prediction coding in cylindrical and spherical projections using SVM-OSSMultimedia Tools and Applications10.1007/s11042-014-2055-674:4(1511-1535)Online publication date: 1-Feb-2015
https://dl.acm.org/doi/10.1007/s11042-014-2055-6
Gao MChen YLiu QHuang CLi ZZhang D(2015)Three-Dimensional Path Planning and Guidance of Leg Vascular Based on Improved Ant Colony Algorithm in Augmented RealityJournal of Medical Systems10.1007/s10916-015-0315-239:11(1-11)Online publication date: 1-Nov-2015
https://dl.acm.org/doi/10.1007/s10916-015-0315-2
Huang HWu SCohen-Or DGong MZhang HLi GChen B(2013)L1-medial skeleton of point cloudACM Transactions on Graphics10.1145/2461912.246191332:4(1-8)Online publication date: 21-Jul-2013
https://dl.acm.org/doi/10.1145/2461912.2461913
He ZLiang XZhao Q(2012)A novel skeletonization and animation approach for point modelsTransactions on Edutainment VII10.5555/2231115.2231129(139-150)Online publication date: 1-Jan-2012
https://dl.acm.org/doi/10.5555/2231115.2231129
Show More Cited By

View Options

View options

Media

Figures

Other

Tables

View Issue’s Table of Contents